Question

If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is
(a) 5
(b) 6
(c) 7
(d) 8

Answer 1

(c) 7

Mean of 5 observations = 11
We know:
$$\begin{gathered} \mathrm{Mean}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{observations}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{observations}} \\ \Rightarrow 11=\frac{x+x+2+x+4+x+6+x+8}{5} \\ \Rightarrow 11=\frac{5x+20}{5} \\ \Rightarrow 5x+20=55 \\ \Rightarrow 5x=35 \\ \Rightarrow x=7 \end{gathered}$$